Something that loses a fixed fraction of itself per unit time decays exponentially: radioactive nuclei, a cooling cup, a discharging capacitor.
The computer can't follow the smooth curve exactly. It takes steps of size dt, guessing where the curve goes next. Euler uses only the slope at the start of each step, so it keeps overshooting. RK4 samples the slope four times per step and is far more accurate for the same dt.
Make dt large with Euler and watch the numerical curve oscillate, then blow up. That's a numerical instability, not physics.